Cylindric algebra

The notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic. This is comparable to the role Boolean algebras play for propositional logic. Indeed, cylindric algebras are Boolean algebras equipped with additional cylindrification operations that model quantification.

Recently, cylindric algebras have been generalized to the many-sorted case, which allows for a better modeling of the duality between first-order formulas and terms.

See also

• Abstract algebraic logic

References

• Henkin, L. and Monk, J.D. and Tarski, A. (1971) Cylindric Algebras, Part I. North-Holland. ISBN 978-0-7204-2043-2.
• C. Caleiro and R. Gonçalves. On the algebraization of many-sorted logics. Preprint, SQIG - IT and IST, 1049-001 Lisboa, Portugal, 2006. Submitted for publication.